N.H. Rev. Stat. Ann. § 45:2

The city councils shall meet in convention on the day appointed by law or ordinance for that purpose, and the city clerk, having entered upon the record the number of votes given in each ward for every person voted for as mayor, shall lay before the convention the returns of such votes, and the convention shall examine the same and declare the person who has the largest number of votes to be elected mayor, and cause him to be notified of his election.